Fine Gael Senator Catherine Noone is calling for a statutory duty of care for social media companies.
The Dublin senator believes more needs to be done to tackle online abuse and harassment.
A duty of care would require companies to adhere to a certain standard to tackle online abuse.
Senator Noone claims that companies should be required to act "in an effective, efficient and timely manner to remove abusive content".
She argued: “Recent reports in the UK show that 1 in 5 social media users have suffered harassment, abuse, bullying or fraud. This highlights the extent of the problem and why action must be taken to prevent the situation deteriorating.
"Be it adults or children, it's a huge issue - and something that I feel is getting worse every day on social media. Clearly, something needs to be done about it."
She added: "Existing requirements for removal of content already provide for terror related issues. I believe this should now be expanded to cover abuse, harassment and fraud."
Research published last year revealed that more than one in 10 school children have experienced cyber bullying.